<h2>Problem 231</h2>
<div style="color:#666;font-size:80%;">06 February 2009</div><br />
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<p>The binomial coefficient <img src="" style="display:none;" alt="^(" /><sup>10</sup><img src="" style="display:none;" alt=")" />C<img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" /> = 120.<br />
120 = 2<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> 3 <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> 5 = 2 <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> 2 <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> 2 <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> 3 <img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' /> 5, and 2 + 2 + 2 + 3 + 5 = 14.<br />
So the sum of the terms in the prime factorisation of <img src="" style="display:none;" alt="^(" /><sup>10</sup><img src="" style="display:none;" alt=")" />C<img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" /> is 14.
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Find the sum of the terms in the prime factorisation of <img src="" style="display:none;" alt="^(" /><sup>20000000</sup><img src="" style="display:none;" alt=")" />C<img src="" style="display:none;" alt="_(" /><sub>15000000</sub><img src="" style="display:none;" alt=")" />.
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